The extraordinary diversity of life has evolved alongside major changes in Earth’s climate and geography and understanding this link is one of the key goals of evolutionary biology. Major advances in methods and the availability of ‘big data’ products have made broad scale tests of the paleoenvironmental drivers of biodiversity possible for the first time. In this talk, I’ll introduce a new approach to study the evolution of biodiversity – mechanistic eco-evolutionary models (MEEMs). MEEMs combine models of the biological diversification of populations and species with changes in climate and tectonics to experimentally explore how diversity, endemism and biogeographic structure evolve over deep timescales. I’ll illustrate this exciting new field with a case study of faunal exchange between Asia and Australia across Wallace’s Line – one of biogeography’s great enigmas.